A139201 -id:A139201

Search: a139201 -id:a139201

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A082671

Numbers n such that (n!-2)/2 is a prime.

+10
20

3, 4, 5, 6, 9, 31, 41, 373, 589, 812, 989, 1115, 1488, 1864, 1918, 4412, 4686, 5821, 13830

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

(4!-2)/2 = 11 is a prime.

MATHEMATICA

Select[Range[0, 14000], PrimeQ[(#! - 2) / 2] &] (* Vincenzo Librandi, Feb 18 2015 *)

PROG

(PARI) xfactpk(n, k=2) = { for(x=2, n, y = (x!-k)/k; if(isprime(y), print1(x", ")) ) }

(Magma) [n: n in [1..600]| IsPrime((Factorial(n)-2) div 2)]; // Vincenzo Librandi, Feb 18 2015

CROSSREFS

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199, A139200, A139201, A139202, A139203, A139204, A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071

KEYWORD

hard,more,nonn

AUTHOR

Cino Hilliard, May 18 2003

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

Edited by T. D. Noe, Oct 30 2008

STATUS

approved

A139199

Numbers k such that (k!-4)/4 is prime.

+10
20

4, 5, 6, 7, 8, 10, 15, 18, 23, 157, 165, 183, 184, 362, 611, 908, 2940, 6875, 9446, 16041

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Numbers k such that (k!-m)/m is prime:

for m=1 see A002982

for m=2 prime or pseudoprime see A082671

for m=3 see A139056

for m=4 see A139199

for m=5 see A139200

for m=6 see A139201

for m=7 see A139202

for m=8 see A139203

for m=9 see A139204

for m=10 see A139205

a(17) > 2000 - Ray G. Opao, Sep 30 2008

a(21) > 25000 - Robert Price, Sep 25 2016

LINKS

Table of n, a(n) for n=1..20.

MATHEMATICA

a = {}; Do[If[PrimeQ[(n! - 4)/4], Print[a]; AppendTo[a, n]], {n, 1, 184}]; a (*Artur Jasinski*)

PROG

(PARI) is(n)=n>3 && isprime(n!/4-1) \\ Charles R Greathouse IV, Apr 29 2015

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

KEYWORD

hard,more,nonn

AUTHOR

Artur Jasinski, Apr 11 2008

EXTENSIONS

a(15)-a(16) from Ray G. Opao, Sep 30 2008

a(17) from Serge Batalov, Feb 18 2015

a(18)-a(20) from Robert Price, Sep 25 2016

STATUS

approved

A290119

Primes of the form k! / 6 - 1.

+10
3

3, 19, 839, 6719, 6652799, 14529715199, 3487131647999, 59281238015999, 1067062284287999, 405483668029439999, 10069210510562305939559188678085666251210751999999999, 5069015533618896340602101361010794807396273594826751999999999999

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Robert Price, Table of n, a(n) for n = 1..14

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

MATHEMATICA

Select[Table[k! / 6 - 1, {k, 4, 100}], PrimeQ[#]&]

CROSSREFS

Cf. A139176, A139201.

KEYWORD

nonn,changed

AUTHOR

Robert Price, Jul 19 2017

EXTENSIONS

3, 19 inserted by Georg Fischer, Dec 05 2024

STATUS

approved

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